A search for QCD-instanton-induced events in deep inelastic ep scattering has been performed with the ZEUS detector at the HERA collider, using data corresponding to an integrated luminosity of 38 pb(-1). A kinematic range defined by cuts on the photon virtuality, Q(2) > 120 GeV2, and on the Bjorken scaling variable, x > 10(-3), has been investigated. The QCD-instanton induced events were modelled by the Monte Carlo generator QCDINS. A background-independent, conservative 95\% confidence level upper limit for the instanton cross section of 26 pb is obtained, to be compared with the theoretically expected value of 8.9 pb.